McVey scored in the seventh minute of added time, firing one just under the crossbar.
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Gonzalo Higuain had a trick for Miami (7-10-5, 26 points), which is 1-3-2 in its past six games.
Cincinnati (7-8-8, 29 points) played to a draw for the sixth time in the past seven matches (0-1-6).
Higuain gave Miami a 1-0 lead in the 23rd minute, burying a strike into the top right corner on a free kick.
Higuain put Miami back in front in the 37th minute. Alejandro Pozuelo spotted the veteran with space through the Cincinnati defenders and Higuain went around goalkeeper Roman Celentano, who came off his line, before putting the ball into the open net for a 2-1 lead.
It was Brenner again with the response for the visitors, getting behind the Miami defense and striking into the left corner from the middle of the box to tie it 2-2 in the 40th minute.
Miami was awarded a penalty in first-half stoppage time after video review showed Tyler Blackett fouled midfielder Jean Mota in the box. It was Higuain again who delivered, completing the hat trick on the ensuing kick from the spot, putting the home side ahead 3-2.
Higuain, who entered the match with four goals on the season, has scored seven of his 20 career MLS goals against Cincinnati.
Pozuelo scored in the 49th minute to give Miami a two-goal advantage but the goal was overturned after video review showed Robert Taylor was offside.
Brandon Vazquez tied it 3-3 in the 81st minute, striking quickly from right in front off a feed from Alvaro Barreal.
Vazquez made it 4-3 Cincinnati in the 86th minute, taking a cross from Barreal at the top of the goal area.